Mass transport effect

Since electrode reactions are heterogeneous chemical processes with transference of charge across the interface, for a net reaction to take place at commensurable rate reactants and products must be transported to and from the electrode surface to sustain a net flux and thus an electrical current across the electrode—electrolyte interface. 

There are three kinds of mass transport process relevant to electrode reactions migration, convection and diffusion. The Nernst—Planck equation 

Both the steady state and transient electrode reaction kinetic data obtained experimentally may contain contributions from the charge transfer kinetics as well as mass transport effects. 

Since reaction rates can be varied by several orders of magnitude with a relatively small change in electrode potential, transport steps may become rate-limiting. It is essential to separate those contributions to 

In practical applications, where the maximum yield of a product or electricity in electrochemical energy conversion systems at the lowest energy cost is desirable, the rate of mass transport should be fast enough in order not to limit the overall rate of the process. For electroanalytical applications, such as polarography or gas sensors, on the other hand, the reaction must be limited by the transport of the reactant since the bulk concentration which is of interest is evaluated from the limiting con-vective-diffusional current. 

---

Compton R G, Ekiund J C, Page S D, Mason T J and Walton D J 1996 Voltammetry in the presence of ultrasound mass transport effects J. Appl. Electrochem. 26 775... 

A detailed study on velocity profiles, pressure drop and mass transport effects is given in [3]. This, in quantitative terms, precisely underlines the advantages (and limits) of the porous-polymer-rod micro reactor concept. 

Figure 5.17 Schematic diagram of the effect of mixing on the concentration of substrate in the liquid and solid phases of a triphasic reaction a represents a reaction that is limited only by the intrinsic reactivity b represents a reaction that is limited by a combination of intrinsic reactivity and mass transport effects c represents a reaction which is limited by mass transport only...

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

It must be emphasized that the above considerations were made in the absence of reaction. Interfacial mass transfer followed by reaction requires further consideration. The Hatta regimes classify transfer-reaction situations into infinitely slow transport compared to reaction (Hatta category A) to infinitely fast transport compared to reaction (Hatta category H) [42]. In the first case all reaction occurs at the interface and in the second all reaction occurs in the bulk fluid. Homogenous catalytic hydrogenations, carbonylations etc. require consideration of this issue. An extreme example of the severity of mass transport effects on reactivity and selectivity in hydroformylation has been provided by Chaudari [43]. Further general discussions for homogeneous catalysis can be found elsewhere [39[. 

Carbon-based catalysts have also been considered for the methane decomposition reaction. Yoon and co-workers have recently investigated the kinetics of methane decomposition on activated carbons as well as on carbon blacks.In case of activated carbons the authors observed mass transport effects in the catalyst particles and also significant pore mouth plugging. The reaction order was found to be 0.5 and the activation energy was found to be 200 kJ/mol for the different activated carbon samples. On the other hand, for... 

Comparison of eqns. (56) and (58) shows the analogy in the mass transport effects in electrode reaction kinetics and homogeneous second-order fast reactions in solution. 

Because rates of reduction by Fe° vary considerably over the range of treatable contaminants, it is possible that there is a continuum of kinetic regimes from purely reaction controlled, to intermediate, to purely mass transport controlled. Fig. 9 illustrates the overlap of estimated mass transport coefficients (kmt) and measured rate coefficients (kSA). The values of kSA are, in most cases, similar to or slower than the kmi values estimated for batch and column reactors. The slower kSA values suggest that krxu < kml, and therefore removal of most contaminants by Fe° should be reaction limited or only slightly influenced by mass transport effects (i.e., an intermediate kinetic regime). 

Scherer MM, Johnson K, Westall JC, Tratnyek PG. Mass transport effects on the kinetics of nitrobenzene reduction by iron metal. Environ Sci Technol 2001 35 2804-2811. 

In order to describe mass transport effects it is necessary to have an understanding of the measurements used to quantify... 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

A detailed examination of the mass transport effects of the HMRDE has been made. At low rotation speeds and for small amplitude modulations (as defined in Section 10.3.6.2) the response of the current is found to agree exactly with that predicted by the steady-state Levich theory (equations (10.15)-(10.17)) [27, 36, 37]. Theoretical and experimental application of the HMRDE, under these conditions, to cases where the electrode reaction rate constant was comparable to the mass-transfer coefficient has also been made [36]. At higher rotation speeds and/or larger amplitude modulations, the observed current response deviated from the expected Levich behaviour. 

Mass transport effects have to be considered to understand the catalyst s reactivity. 

As described in Section 4.1.1.2, in most catalytic reactions, the reactant molecules diffuse through a boundary layer and through the pores to the active center, react, and diffuse back. If the velocity of any of these two diffusion processes is smaller than the conversion of the reactants at the active center, the overall reaction rate for the whole process is limited by the mass transport and not by the chemical reaction. If the reaction is influenced by mass transport effects, a comparison of the catalytic activity of different catalysts is impossible ... 

When the potential step is small and the system is chemically reversible three cases of interest are analyzed. First, when the reaction is kinetically sluggish (electrochemi-cally -> irreversible or quasireversible) and the -> mass transport effects are negligible. 

These contributions from the various mass transport effects have been formalized in terms of the dependency of he i on Vj for a particular biosolute Pj through the well-known van Deemter-Knox relationships, which take the form... 

---